\documentclass[UTF8]{book}
\setcounter{secnumdepth}{3}
\usepackage{url}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{color}

\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\theoremstyle{plain}
\ifx\thechapter\undefined
	\newtheorem{Theorem}{定理}
\else
	\newtheorem{Theorem}{定理}[chapter]
\fi
\newtheorem{Lemma}[Theorem]{引理}
\newtheorem{Corollary}[Theorem]{推论}
\newtheorem{Proposition}[Theorem]{命题}
\newtheorem{Conjecture}[Theorem]{猜想}
\newtheorem{Fact}[Theorem]{事实}

\theoremstyle{definition}
\newtheorem{Definition}[Theorem]{定义}
\newtheorem{Example}[Theorem]{例}
\newtheorem{Problem}[Theorem]{问题}
\newtheorem{Exercise}[Theorem]{习题}
\newtheorem{Claim}[Theorem]{断言}

\theoremstyle{remark}
\newtheorem{Note}[Theorem]{注记}

\newenvironment{Proof}[1][证明]
{\noindent\normalfont {\bfseries #1}}{□}


\makeatother